Question

Convert the following to the equivalent measures indicated. \(6,172 \mathrm{~g}=\) ______ \(\mathrm{kg}\)

Short answer

6,172 g is equal to 6.172 kg.

Step-by-step solution

Understand the Conversion Factor

To convert grams (g) to kilograms (kg), we need to understand the conversion factor. By definition, 1 kilogram is equal to 1,000 grams. This means that we need to divide the number of grams by 1,000 to get the equivalent in kilograms.

Perform the Conversion

Using the conversion factor from Step 1, we divide 6,172 grams by 1,000 to convert it to kilograms. The calculation is as follows: \[6,172 \text{ g} \times \frac{1 \text{ kg}}{1,000 \text{ g}} = 6.172 \text{ kg}\]

Check the Solution

Check the calculation to ensure accuracy by multiplying back to check: \[6.172 \text{ kg} \times 1,000 \text{ g/kg} = 6,172 \text{ g}\]This confirms that our conversion was done correctly, as it matches the original amount in grams.

Key concepts

Conversion Factor

In mathematics and science, a conversion factor is a number used to change units from one measurement system to another while preserving the actual value. Conversion factors are ratios that express the same quantity in different units. They can be immensely helpful for converting between measurement systems, such as from grams to kilograms.To find a conversion factor, you need to know the equivalence of the two units. For example:

• 1 kilogram is equal to 1,000 grams.
• Therefore, the conversion factor from grams to kilograms is \(\frac{1 \text{ kg}}{1,000 \text{ g}}\).

Using conversion factors simplifies the conversion process as it involves multiplying or dividing by that factor, depending on whether you're converting to a larger or smaller unit.

Metric System

The metric system is a universally adopted system of measurement used in most nations around the world. It is based on powers of ten, making calculations and conversions straightforward. Key aspects of the metric system include:

• Standard units (such as meter, liter, and gram) for different types of measurements like length, volume, and mass.
• Use of prefixes like kilo-, centi-, and milli-, to indicate multiples and fractions of these units.
• Consistency and ease of conversion due to its decimal nature.

This system helps maintain uniformity and simplicity across scientific and everyday measurements by reducing the need for complex conversions.

Kilograms to Grams

Converting between kilograms and grams is a common task when dealing with measurements of mass or weight in the metric system. Understanding the relationship between kilograms and grams is essential:

• Kilogram: A larger unit, often used for heavier items or larger quantities.
• Gram: A smaller unit, typically used for lighter objects or smaller amounts.

When you need to convert from kilograms to grams, the relationship is simple:

• Since 1 kg = 1,000 g, to convert kilograms to grams, multiply the number of kilograms by 1,000.
• Conversely, to convert from grams to kilograms, divide the number of grams by 1,000.

This straightforward relationship ensures easy conversion between the two, making it helpful for various scientific and practical applications.